Robust passivity and passification of stochastic fuzzy time-delay systems
Robust passivity and passification of stochastic fuzzy time-delay systems
复制标题
DOI：
10.1016/j.ins.2010.01.003
复制
发表时间：
2010-05
期刊：
影响因子：
--
通讯作者：
Jinling Liang;Zidong Wang;Xiaohui Liu
中科院分区：
文献类型：
--
作者：
Jinling Liang;Zidong Wang;Xiaohui Liu
本文研究了一类时变时滞不确定随机模糊系统的无源性和无源化问题。模糊系统基于 Takagi–Sugeno (T–S) 模型，该模型通常用于用模糊集和模糊推理来表示复杂的非线性系统。为了反映系统更真实的动态行为，同时考虑参数不确定性和随机扰动，其中参数不确定性进入所有系统矩阵，随机扰动以布朗运动的形式给出。我们首先提出期望意义上的鲁棒被动性的定义。然后，利用Lyapunov泛函方法、Itô微分法则和矩阵分析技术，我们建立了几个充分的准则，使得对于所有允许的参数不确定性和随机扰动，闭环随机模糊时滞系统在期望意义上是鲁棒无源的。导出的标准要么与延迟无关，要么与延迟相关，以线性矩阵不等式 (LMI) 表示，可以使用标准数值软件轻松检查。给出了说明性例子来证明所提出的结果的有效性和实用性。
In this paper, the passivity and passification problems are investigated for a class of uncertain stochastic fuzzy systems with time-varying delays. The fuzzy system is based on the Takagi–Sugeno (T–S) model that is often used to represent the complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning. To reflect more realistic dynamical behaviors of the system, both the parameter uncertainties and the stochastic disturbances are considered, where the parameter uncertainties enter into all the system matrices and the stochastic disturbances are given in the form of a Brownian motion. We first propose the definition of robust passivity in the sense of expectation. Then, by utilizing the Lyapunov functional method, the Itô differential rule and the matrix analysis techniques, we establish several sufficient criteria such that, for all admissible parameter uncertainties and stochastic disturbances, the closed-loop stochastic fuzzy time-delay system is robustly passive in the sense of expectation. The derived criteria, which are either delay-independent or delay-dependent, are expressed in terms of linear matrix inequalities (LMIs) that can be easily checked by using the standard numerical software. Illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results.